In a resonator is provided that suppresses a shift of a resonant frequency. The resonator includes a vibration portion that has a base with front and rear ends and multiple vibration arms with fixed ends connected to the front end of the base and that extend away from the front end. Moreover, the resonator includes a frame that at least partially surrounds the vibration portion and one or more holding arms provided between the vibration portion and the frame with first ends connected to the base and the second ends connected to a region of the frame at the front end side relative to the rear end of the base portion.

A resonator is provided that suppresses frequency variations with etching without decreasing the strength of vibration arms. The resonator includes a base portion, a first vibration portion extending from the base portion in a first direction and having a first width, and a second vibration portion extending from the base portion in the first direction with a first gap between the first and second vibration portions and having the first width. The first and second vibration portions perform out-of-plane bending vibration with opposite phases at a predetermined frequency. The predetermined frequency varies in accordance with the first width and the first gap. The ratio of the first gap to the first width is within a range that causes an absolute value of rates of variations in the predetermined frequency with respect to variations in the first width and in the first gap to be not more than about 100 ppm.

In a resonator is provided that suppresses a shift of a resonant frequency. The resonator includes a vibration portion that has a base with front and rear ends and multiple vibration arms with fixed ends connected to the front end of the base and that extend away from the front end. Moreover, the resonator includes a frame that at least partially surrounds the vibration portion and one or more holding arms provided between the vibration portion and the frame with first ends connected to the base and the second ends connected to a region of the frame at the front end side relative to the rear end of the base portion.

A resonator is provided that suppresses frequency variations with etching without decreasing the strength of vibration arms. The resonator includes a base portion, a first vibration portion extending from the base portion in a first direction and having a first width, and a second vibration portion extending from the base portion in the first direction with a first gap between the first and second vibration portions and having the first width. The first and second vibration portions perform out-of-plane bending vibration with opposite phases at a predetermined frequency. The predetermined frequency varies in accordance with the first width and the first gap. The ratio of the first gap to the first width is within a range that causes an absolute value of rates of variations in the predetermined frequency with respect to variations in the first width and in the first gap to be not more than about 100 ppm.

A self-referencing, microelectromechanical system with dual mechanical modes for temperature independent environmental sensing including a resonator configured to resonate in a first fundamental width extensional mode and in a second contour mode, including: an input port; an output port; a top electrode comprising an aluminum chromium layer; a silicon-oxide layer; an aluminum-nitride layer; and an RF ground comprising a silicon layer. Upon passing a signal to the top electrode of the resonator, the top electrode and the RF ground establish an electric field to enable transduction through the piezoelectric, aluminum-nitride layer, and the resonator has adjacent contour modes close in frequency such that mechanical resonances of the resonator in differing resonance modes shift together as a function of temperature, the simultaneous shift of the mechanical resonances remaining constant across the temperature range enabling sensing of various criteria.